Better Numerical Approximation by Durrmeyer Type Operators

Abstract

The main object of this paper is to construct new Durrmeyer type operators which have better features than the classical one. Some results concerning the rate of convergence and asymptotic formulas of the new operator are given. Finally, the theoretical results are analyzed by numerical examples.

Perturbed Bernstein-type operators

“…In this section we study a Durrmeyer variant of the modified Bernstein operators introduced in a recent note of Acu, Gupta and Tachev [3]:…”

On complex modified Bernstein-Stancu operators

“…Hence, they established a new and simple approach to improve the order of approximation of the Bernstein operators. By using their approach, some generalizations of the modified Bernstein operators given by (3) were introduced and investigated approximation properties (see, e.g., [1,3,4,11]). Concerning complex Bernstein polynomials, convergence properties of these operators in various domains in complex plane such as compact disks, ellipses, loops etc.…”

Better approximation of function by $α-$Bernstein-Păltănea operators

“…In [15], Khosravian-Arab et al modified the well known Bernstein operators by using a new approach to improve the degree of approximation. Following this, Acu et al [1] have applied this approach on the Bernstein-Durrmeyer operators. In an another paper [11], same authors have put it on the Bernstein-Kantorovich operators too.…”